Find a 4th Degree Polynomial with Specific Conditions

[utkarshakash]

Homework Statement

Find a polynomial f(x) of degree 4 which increases in the intervals (-∞,1) and (2,3) and decreases in the interval (1,2) and (3,∞) and satisifes the condition f(0)=1

Homework Equations

The Attempt at a Solution

Let f(x)=ax^4+bx^3+cx^2+dx+1
f'(1)=f'(2)=f'(3)=0

But using the above results I get only 3 eqns whereas there are 4 variables.

 

[ehild]

You have to find one polynomial from the infinite many which obey the conditions.

ehild

 

[utkarshakash]

You have to find one polynomial from the infinite many which obey the conditions.

ehild

I still can't figure out.

 

[dirk_mec1]

There are a lot of polynomials which satisfy the requirements. Luckily you only need ONE of them, get it?

 

[HallsofIvy]

What you are being told is that this problem does NOT have a single, unique, answer. You can use the three equations to solve for three of a, b, c, and d, in terms of the other one. Then just arbitrarily choose a value for that one to get one such polynomial out of the infinite number that satisfy these conditions.

 

[LCKurtz]

You have to find one polynomial from the infinite many which obey the conditions.

ehild

I still can't figure out.

That doesn't help us to help you. Nor does it show any effort.

What you are being told is that this problem does NOT have a single, unique, answer. You can use the three equations to solve for three of a, b, c, and d, in terms of the other one. Then just arbitrarily choose a value for that one to get one such polynomial out of the infinite number that satisfy these conditions.

Halls just told you how to work the problem. Have you tried that?